Page 321 - Introduction to chemical reaction engineering and kinetics

302 Chapter 12: Batch Reactors (BR)

state, we assume ideal-gas behavior. Thus, for ( -rA),

Since this is a gas-phase reaction, and the total number of moles changes, the volume
changes as the reaction progresses. We use a stoichiometric table to determine the effect
of fA on V.

Species Initial Change Final
moles An moles

A nh -nAofA nA,(l - fA)
B 0 nAofA nAofA
C 0 nAo.fA nAofA

total: nAo nAofA nAo(l + fA)

If the gas phase is ideal, V = n,RTIP, and in this case, R, T, and P are constant. Therefore,

V nAo(l + fA)
v,= nA0

or
v = V,(l + f*X (W

where V, is the initial volume of the system.
Substituting for (-?-A) from (A) and for V from (B) in equation 12.3-2, and simplifying,
we obtain:

To integrate, we let a = 1 - fA; then, fA = 1 - ff, and dfA = -da. The integral is:

0.25 a - 2
(y2 da = ln(0.25) + 6 = 4.61
I1
Therefore, t = 10 L X 4.61/(0.023 L mol-l s-l X 5.0 mol) = 400 s

12.3.2.3 Control of Heat Transfer to Maintain Isothermal Conditions
In certain circumstances, it may be desirable to maintain nearly isothermal conditions,
even if the reaction is significantly exothermic or endothermic. In the absence of any
attempt to control T, it may become too high for product stability or too low for reac-
tion rate. If control of T is required, a cooling or heating coil or jacket can be added
to the reactor to balance the energy generated or consumed by the reaction. The coil
temperature (T,) is adjusted to control the rate of heat transfer (b) to achieve (nearly)
isothermal conditions. T, usually varies as the reaction proceeds, because the rate of
reaction, (-rA), and hence AH, is a function of time. The relationship between T, or 6
and fA can be determined by combining the material and energy balances.